A desire exists for a pump of the above-mentioned type which is compact and which may be brought on bicycles, on camping trips and for other purposes. Pumps of the above type are known from e.g. U.S. Pat. No. 5,127,808. Even though this known pump is rather compact and is able to be brought for use independent of an external power supply, it has a radial dimension which is relatively large. Thus the orientation of the toothed wheel about an axis being parallel with the longitudinal axis of the pump contributes to the relatively large radial dimension of the pump. Moreover, the pump is disadvantageous in that it is rather complicated and consists of a large number of specialized individual parts. Moreover, the pump is disadvantageous as it may not be used for one hand operation. Thus the nozzle is affixed to the compressor of the pump through a flexible air hose.